Print the longest palindromic prefix of a given string
Last Updated :
07 Jul, 2021
Given a string str, the task is to find the longest palindromic prefix of the given string.
Examples:
Input: str = "abaac"
Output: aba
Explanation:
The longest prefix of the given string which is palindromic is "aba".
Input: str = "abacabaxyz"
Output: abacaba
Explanation:
The prefixes of the given string which is palindromic are "aba" and "abacabaxyz".
But the longest of among two is "abacabaxyz".
Naive Approach: The idea is to generate all the substring of the given string from the starting index and check whether the substrings are palindromic or not. The palindromic string with a maximum length is the resultant string.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the longest prefix
// which is palindromic
void LongestPalindromicPrefix(string s)
{
// Find the length of the given string
int n = s.length();
// For storing the length of longest
// prefix palindrome
int max_len = 0;
// Loop to check the substring of all
// length from 1 to N which is palindrome
for (int len = 1; len <= n; len++) {
// String of length i
string temp = s.substr(0, len);
// To store the reversed of temp
string temp2 = temp;
// Reversing string temp2
reverse(temp2.begin(), temp2.end());
// If string temp is palindromic
// then update the length
if (temp == temp2) {
max_len = len;
}
}
// Print the palindromic string of
// max_len
cout << s.substr(0, max_len);
}
// Driver Code
int main()
{
// Given string
string str = "abaab";
// Function Call
LongestPalindromicPrefix(str);
}
// Java program for the above approach
import java.util.*;
class GFG{
// Function to find the longest prefix
// which is palindromic
static void LongestPalindromicPrefix(String s)
{
// Find the length of the given String
int n = s.length();
// For storing the length of longest
// prefix palindrome
int max_len = 0;
// Loop to check the subString of all
// length from 1 to N which is palindrome
for (int len = 1; len <= n; len++)
{
// String of length i
String temp = s.substring(0, len);
// To store the reversed of temp
String temp2 = temp;
// Reversing String temp2
temp2 = reverse(temp2);
// If String temp is palindromic
// then update the length
if (temp.equals(temp2))
{
max_len = len;
}
}
// Print the palindromic String of
// max_len
System.out.print(s.substring(0, max_len));
}
static String reverse(String input)
{
char[] a = input.toCharArray();
int l, r = a.length - 1;
for (l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return String.valueOf(a);
}
// Driver Code
public static void main(String[] args)
{
// Given String
String str = "abaab";
// Function Call
LongestPalindromicPrefix(str);
}
}
// This code is contributed by Rajput-Ji
# Python3 program for the above approach
# Function to find the longest prefix
# which is palindrome
def LongestPalindromicPrefix(string):
# Find the length of the given string
n = len(string)
# For storing the length of longest
# Prefix Palindrome
max_len = 0
# Loop to check the substring of all
# length from 1 to n which is palindrome
for length in range(0, n + 1):
# String of length i
temp = string[0:length]
# To store the value of temp
temp2 = temp
# Reversing the value of temp
temp3 = temp2[::-1]
# If string temp is palindromic
# then update the length
if temp == temp3:
max_len = length
# Print the palindromic string
# of max_len
print(string[0:max_len])
# Driver code
if __name__ == '__main__' :
string = "abaac";
# Function call
LongestPalindromicPrefix(string)
# This code is contributed by virusbuddah_
// C# program for the above approach
using System;
class GFG{
// Function to find the longest prefix
// which is palindromic
static void longestPalindromicPrefix(String s)
{
// Find the length of the given String
int n = s.Length;
// For storing the length of longest
// prefix palindrome
int max_len = 0;
// Loop to check the subString of all
// length from 1 to N which is palindrome
for (int len = 1; len <= n; len++)
{
// String of length i
String temp = s.Substring(0, len);
// To store the reversed of temp
String temp2 = temp;
// Reversing String temp2
temp2 = reverse(temp2);
// If String temp is palindromic
// then update the length
if (temp.Equals(temp2))
{
max_len = len;
}
}
// Print the palindromic String of
// max_len
Console.Write(s.Substring(0, max_len));
}
static String reverse(String input)
{
char[] a = input.ToCharArray();
int l, r = a.Length - 1;
for (l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return String.Join("",a);
}
// Driver Code
public static void Main(String[] args)
{
// Given String
String str = "abaab";
// Function Call
longestPalindromicPrefix(str);
}
}
// This code is contributed by amal kumar choubey
<script>
// JavaScript program for the above approach
// Function to find the longest prefix
// which is palindromic
function LongestPalindromicPrefix(s)
{
// Find the length of the given String
let n = s.length;
// For storing the length of longest
// prefix palindrome
let max_len = 0;
// Loop to check the subString of all
// length from 1 to N which is palindrome
for (let len = 1; len <= n; len++)
{
// String of length i
let temp = s.substring(0, len);
// To store the reversed of temp
let temp2 = temp;
// Reversing String temp2
temp2 = reverse(temp2);
// If String temp is palindromic
// then update the length
if (temp == temp2)
{
max_len = len;
}
}
// Print the palindromic String of
// max_len
document.write(s.substring(0, max_len));
}
function reverse(input)
{
let a = input.split('');
let l, r = a.length - 1;
for (l = 0; l < r; l++, r--)
{
let temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return a.join("");
}
// Given String
let str = "abaab";
// Function Call
LongestPalindromicPrefix(str);
</script>
Time Complexity: O(N2), where N is the length of the given string.
Efficient Approach: The idea is to use preprocessing algorithm KMP Algorithm. Below are the steps:
- Create a temporary string(say str2) which is:
str2 = str + '?' reverse(str);
- Create an array(say lps[]) of size of length of the string str2 which will store the longest palindromic prefix which is also a suffix of string str2.
- Update the lps[] by using preprocessing algorithm of KMP Search Algorithm.
- lps[length(str2) - 1] will give the length of the longest palindromic prefix string of the given string str.
Below is the implementation of the above approach:
C++
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to find the longest prefix
// which is palindromic
void LongestPalindromicPrefix(string str)
{
// Create temporary string
string temp = str + '?';
// Reverse the string str
reverse(str.begin(), str.end());
// Append string str to temp
temp += str;
// Find the length of string temp
int n = temp.length();
// lps[] array for string temp
int lps[n];
// Initialise every value with zero
fill(lps, lps + n, 0);
// Iterate the string temp
for (int i = 1; i < n; i++) {
// Length of longest prefix
// till less than i
int len = lps[i - 1];
// Calculate length for i+1
while (len > 0
&& temp[len] != temp[i]) {
len = lps[len - 1];
}
// If character at current index
// len are same then increment
// length by 1
if (temp[i] == temp[len]) {
len++;
}
// Update the length at current
// index to len
lps[i] = len;
}
// Print the palindromic string of
// max_len
cout << temp.substr(0, lps[n - 1]);
}
// Driver's Code
int main()
{
// Given string
string str = "abaab";
// Function Call
LongestPalindromicPrefix(str);
}
// Java program for the above approach
import java.util.*;
class GFG{
// Function to find the longest
// prefix which is palindromic
static void LongestPalindromicPrefix(String str)
{
// Create temporary String
String temp = str + '?';
// Reverse the String str
str = reverse(str);
// Append String str to temp
temp += str;
// Find the length of String temp
int n = temp.length();
// lps[] array for String temp
int []lps = new int[n];
// Initialise every value with zero
Arrays.fill(lps, 0);
// Iterate the String temp
for(int i = 1; i < n; i++)
{
// Length of longest prefix
// till less than i
int len = lps[i - 1];
// Calculate length for i+1
while (len > 0 && temp.charAt(len) !=
temp.charAt(i))
{
len = lps[len - 1];
}
// If character at current index
// len are same then increment
// length by 1
if (temp.charAt(i) == temp.charAt(len))
{
len++;
}
// Update the length at current
// index to len
lps[i] = len;
}
// Print the palindromic String
// of max_len
System.out.print(temp.substring(0, lps[n - 1]));
}
static String reverse(String input)
{
char[] a = input.toCharArray();
int l, r = a.length - 1;
for(l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return String.valueOf(a);
}
// Driver Code
public static void main(String[] args)
{
// Given String
String str = "abaab";
// Function Call
LongestPalindromicPrefix(str);
}
}
// This code is contributed by Rajput-Ji
# Python3 program for the above approach
# Function to find the longest prefix
# which is palindromic
def LongestPalindromicPrefix(Str):
# Create temporary string
temp = Str + "?"
# Reverse the string Str
Str = Str[::-1]
# Append string Str to temp
temp = temp + Str
# Find the length of string temp
n = len(temp)
# lps[] array for string temp
lps = [0] * n
# Iterate the string temp
for i in range(1, n):
# Length of longest prefix
# till less than i
Len = lps[i - 1]
# Calculate length for i+1
while (Len > 0 and temp[Len] != temp[i]):
Len = lps[Len - 1]
# If character at current index
# Len are same then increment
# length by 1
if (temp[i] == temp[Len]):
Len += 1
# Update the length at current
# index to Len
lps[i] = Len
# Print the palindromic string
# of max_len
print(temp[0 : lps[n - 1]])
# Driver Code
if __name__ == '__main__':
# Given string
Str = "abaab"
# Function call
LongestPalindromicPrefix(Str)
# This code is contributed by himanshu77
// C# program for the above approach
using System;
class GFG{
// Function to find the longest
// prefix which is palindromic
static void longestPalindromicPrefix(String str)
{
// Create temporary String
String temp = str + '?';
// Reverse the String str
str = reverse(str);
// Append String str to temp
temp += str;
// Find the length of String temp
int n = temp.Length;
// lps[] array for String temp
int []lps = new int[n];
// Iterate the String temp
for(int i = 1; i < n; i++)
{
// Length of longest prefix
// till less than i
int len = lps[i - 1];
// Calculate length for i+1
while (len > 0 && temp[len] != temp[i])
{
len = lps[len - 1];
}
// If character at current index
// len are same then increment
// length by 1
if (temp[i] == temp[len])
{
len++;
}
// Update the length at current
// index to len
lps[i] = len;
}
// Print the palindromic String
// of max_len
Console.Write(temp.Substring(0, lps[n - 1]));
}
static String reverse(String input)
{
char[] a = input.ToCharArray();
int l, r = a.Length - 1;
for(l = 0; l < r; l++, r--)
{
char temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return String.Join("", a);
}
// Driver Code
public static void Main(String[] args)
{
// Given String
String str = "abaab";
// Function Call
longestPalindromicPrefix(str);
}
}
// This code is contributed by Rajput-Ji
<script>
// Javascript program for the above approach
// Function to find the longest
// prefix which is palindromic
function longestPalindromicPrefix(str)
{
// Create temporary String
let temp = str + '?';
// Reverse the String str
str = reverse(str);
// Append String str to temp
temp += str;
// Find the length of String temp
let n = temp.length;
// lps[] array for String temp
let lps = new Array(n);
lps.fill(0);
// Iterate the String temp
for(let i = 1; i < n; i++)
{
// Length of longest prefix
// till less than i
let len = lps[i - 1];
// Calculate length for i+1
while (len > 0 && temp[len] != temp[i])
{
len = lps[len - 1];
}
// If character at current index
// len are same then increment
// length by 1
if (temp[i] == temp[len])
{
len++;
}
// Update the length at current
// index to len
lps[i] = len;
}
// Print the palindromic String
// of max_len
document.write(temp.substring(0, lps[n - 1]));
}
function reverse(input)
{
let a = input.split('');
let l, r = a.length - 1;
for(l = 0; l < r; l++, r--)
{
let temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return a.join("");
}
// Driver code
// Given String
let str = "abaab";
// Function Call
longestPalindromicPrefix(str);
// This code is contributed by mukesh07
</script>
Time Complexity: O(N), where N is the length of the given string.
Auxiliary Space: O(N), where N is the length of the given string.
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